Peaks, Valleys, and Blur: Optimization and Uncertainty Quantification

I describe the integration of parameter continuation techniques with variational calculus and covariance analysis for purposes of design optimization and uncertainty quantification along families of periodic and quasi-periodic orbits of nonlinear dynamical systems, as well as solutions to more general classes of multi-segment boundary-value problems, including those coupled through time delays. This integration has been realized in the Matlab-based software package COCO by supporting the automated construction of adjoint contributions to the corresponding Karush-Kuhn-Tucker conditions. I describe the general software design principles and illustrate the methodology on toy problems that capture the full complexity of the approach while also allowing for analytical and/or simulation-based validation.